813 research outputs found
A volume-based hydrodynamic approach to sound wave propagation in a monatomic gas
We investigate sound wave propagation in a monatomic gas using a volume-based
hydrodynamic model. In Physica A vol 387(24) (2008) pp6079-6094, a microscopic
volume-based kinetic approach was proposed by analyzing molecular spatial
distributions; this led to a set of hydrodynamic equations incorporating a
mass-density diffusion component. Here we find that these new mass-density
diffusive flux and volume terms mean that our hydrodynamic model, uniquely,
reproduces sound wave phase speed and damping measurements with excellent
agreement over the full range of Knudsen number. In the high Knudsen number
(high frequency) regime, our volume-based model predictions agree with the
plane standing waves observed in the experiments, which existing kinetic and
continuum models have great difficulty in capturing. In that regime, our
results indicate that the "sound waves" presumed in the experiments may be
better thought of as "mass-density waves", rather than the pressure waves of
the continuum regime.Comment: Revised to aid clarification (no changes to presented model); typos
corrected, figures added, paper title change
A continuum model of gas flows with localized density variations
We discuss the kinetic representation of gases and the derivation of macroscopic equations governing the thermomechanical behavior of a dilute gas viewed at the macroscopic level as a continuous medium. We introduce an approach to kinetic theory where spatial distributions of the molecules are incorporated through a mean-free-volume argument. The new kinetic equation derived contains an extra term involving the evolution of this volume, which we attribute to changes in the thermodynamic properties of the medium. Our kinetic equation leads to a macroscopic set of continuum equations in which the gradients of thermodynamic properties, in particular density gradients, impact on diffusive fluxes. New transport terms bearing both convective and diffusive natures arise and are interpreted as purely macroscopic expansion or compression. Our new model is useful for describing gas flows that display non-local-thermodynamic-equilibrium (rarefied gas flows), flows with relatively large variations of macroscopic properties, and/or highly compressible fluid flows
Lattice Boltzmann scheme for relativistic fluids
A Lattice Boltzmann formulation for relativistic fluids is presented and
numerically verified through quantitative comparison with recent hydrodynamic
simulations of relativistic shock-wave propagation in viscous quark-gluon
plasmas. This formulation opens up the possibility of exporting the main
advantages of Lattice Boltzmann methods to the relativistic context, which
seems particularly useful for the simulation of relativistic fluids in
complicated geometries.Comment: Submitted to PR
Continuum description of finite-size particles advected by external flows. The effect of collisions
The equation of the density field of an assembly of macroscopic particles
advected by a hydrodynamic flow is derived from the microscopic description of
the system. This equation allows to recognize the role and the relative
importance of the different microscopic processes implicit in the model: the
driving of the external flow, the inertia of the particles, and the collisions
among them.
The validity of the density description is confirmed by comparisons of
numerical studies of the continuum equation with Direct Simulation Monte Carlo
(DSMC) simulations of hard disks advected by a chaotic flow. We show that the
collisions have two competing roles: a dispersing-like effect and a clustering
effect (even for elastic collisions). An unexpected feature is also observed in
the system: the presence of collisions can reverse the effect of inertia, so
that grains with lower inertia are more clusterized.Comment: Final (strongly modified) version accepted in PRE; 6 pages, 3 figure
Formation and Propagation of Discontinuity for Boltzmann Equation in Non-Convex Domains
The formation and propagation of singularities for Boltzmann equation in
bounded domains has been an important question in numerical studies as well as
in theoretical studies. Consider the nonlinear Boltzmann solution near
Maxwellians under in-flow, diffuse, or bounce-back boundary conditions. We
demonstrate that discontinuity is created at the non-convex part of the grazing
boundary, then propagates only along the forward characteristics inside the
domain before it hits on the boundary again.Comment: 39 pages, 5 Figure
Continuum limit of self-driven particles with orientation interaction
We consider the discrete Couzin-Vicsek algorithm (CVA), which describes the
interactions of individuals among animal societies such as fish schools. In
this article, we propose a kinetic (mean-field) version of the CVA model and
provide its formal macroscopic limit. The final macroscopic model involves a
conservation equation for the density of the individuals and a non conservative
equation for the director of the mean velocity and is proved to be hyperbolic.
The derivation is based on the introduction of a non-conventional concept of a
collisional invariant of a collision operator
A randomised controlled trial of efficacy of cognitive rehabilitation in multiple sclerosis: a cognitive, behavioural, and MRI study
Aim: To explore the efficacy of home-based, computerised, cognitive rehabilitation in patients with multiple sclerosis using neuropsychological assessment and advanced structural and functional magnetic resonance imaging (fMRI).
Methods: 38 patients with MS and cognitive impairment on the Brief International Cognitive Assessment for MS (BICAMS) were enrolled. Patients were randomised to undergo 45 minutes of computerised cognitive rehabilitation using RehaCom software (n = 19) three times weekly for six weeks or to a control condition (n = 19). Neuropsychological and MRI data were obtained at baseline (time 1), following the 6-week intervention (time 2), and after a further twelve weeks (time 3). Cortical activations were explored using fMRI and microstructural changes were explored using quantitative magnetisation transfer (QMT) imaging.
Results: The treatment group showed a greater improvement in SDMT gain scores between baseline and time 2 compared to the control group (p = 0.005). The treatment group exhibited increased activation in the bilateral prefrontal cortex and right temporoparietal regions relative to control group at time 3 (p < 0.05FWE corrected). No significant changes were observed on QMT.
Conclusion: This study supports the hypothesis that home-based, computerised, cognitive rehabilitation may be effective in improving cognitive performance in patients with MS.
Clinical trials registration is ISRCTN54901925
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